Nowadays, the acceleration of electrically charged particles, such as e.g. electrons or protons, is a new and promising field of application of intense terahertz (THz) pulses with frequencies in the range of substantially 0.1-10 THz (as per agreement). Terahertz pulses are conventionally generated by coupling ultrashort light pulses, i.e. light pulses having a pulse width in the femtosecond (fs) to picoseconds (ps) domain, into a crystal with nonlinear optical properties, in general, by means of optical rectification within the crystal. To this end, typically pulses of visible or near infrared pump pulses with the pulse width of several hundred femtoseconds are used.
To achieve efficient terahertz radiation generation, the so called velocity matching condition has to be met. This means that the group velocity of the pump pulse used for the generation has to be equal to the phase velocity of the THz pulse thus generated. If said velocities are close to each other, i.e. the group refraction index of the nonlinear crystal at the frequency of the pumping differs from the refraction index in the THz domain only to a reasonably small extent, fulfilment of this condition may be achieved by known means.
The second order nonlinear optical coefficient of the (crystal) material affects decisively the efficiency of terahertz radiation generation. For some materials, in which said coefficient is high (exceeds, typically, several ten pm/V's) and the aforementioned refraction index difference is also high, terahertz radiation generation with velocity matching becomes unachievable. This is the case for several materials: some semiconductors, such as e.g. gallium-phosphide (GaP), zinc-telluride (ZnTe) and also lithium-niobate (LN) and lithium-tantalate (LT) having exceptionally high (160-170 pm/V) nonlinear optical coefficients, wherein the ratio of the group refraction index at the pump frequency and the phase refraction index in the THz domain is greater than two. A solution for the problem is the tilted-pulse-front technique (see the paper by J. Hebling et al., entitled “Velocity matching by pulse front tilting for large-area THz-pulse generation”; Optics Express; Vol. 10, issue 21, pp. 1161-1166 (2002)). Accordingly, the generation of terahertz radiation is carried out by a light pulse, whose pulse front (intensity front) is at a desired angle (γ) to the wave front. As the THz beam generated propagates perpendicularly to the tilted pulse front, due to said velocity matching condition, the projection of the group velocity vp,cs of pumping onto the direction of THz radiation propagation has to be equal to the phase velocity vTHz,f of the THz beam, that is, the relation ofvp,cs cos(γ)=vTHz,f  (1)has to be met. In particular, for pump wavelengths in the near-infrared domain, this relation is satisfied at γ≈63° for LN, γ≈69° for LT, and γ≈22°-29° for ZnTe, respectively.
At present, the highest energy THz pulses with frequencies suitable for particle acceleration (i.e. of about 0.2-1.0 THz) can be generated by means of LN crystals and using the tilted pulse front technique (see the paper by J. A. Fülöp et al., entitled “Efficient generation of THz pulses with 0.4 mJ energy”; Optics Express; Vol. 22, issue 17, pp. 20155-20163 (2014)). The high energy THz radiation sources described in this publication, that produce pulse energies of 0.43 mJ, use a prism shaped LN crystal as the nonlinear optical crystal in each case. The reason for this, on the one hand, is that to minimize the reflection losses, the pump pulse has to enter the crystal perpendicularly and the THz pulse generated has to exit therefrom also perpendicularly. On the other hand, coupling out the THz beam at right angle ensures that the beam is free from angular dispersion that is a very important requirement from the point of view of further utilization. Accordingly, to meet the velocity matching condition (1), the exit plane of the LN crystal has to form a wedge angle with the entry plane of the LN crystal that is equal to the angle γ.
As the wedge angle in the case of LN crystals is large (γ≈63°), at high energy THz generation, making use of the medium for generating THz radiation in the form of a prism is highly detrimental to the quality of the THz beam thus generated, because for a wide pump beam, that is necessary for high energy THz generation, the THz pulses appearing at the two cross-sectionally opposite sides of the pump beam are generated over significantly different lengths, and hence are subject to absorption and dispersion to different extents; moreover, the nonlinear effects are also different in the LN crystal at said locations of generation. Therefore, the intensity of, as well as the temporal electric field profile within the THz pulses generated at portions located symmetrically at the two sides of the pump pulse are significantly different, i.e. a bad quality, highly asymmetric THz beam is obtained. An important criterion for carrying out particle acceleration efficiently is the precise synchronization between the particle to be accelerated and the pulse with a field strength of controllable temporal profile to be used for the acceleration. Hence, the thus obtainable asymmetric THz beam of low beam quality is unfit for the synchronization, and thus for the efficient particle acceleration.
In case of the conventional tilted-pulse-front technique, the pulse front tilt of the pump beam is obtained by diffraction on a (reflection or transmission) optical grating arranged in the beam path. Then the beam is guided, through a lens or a telescope by means of imaging, into a nonlinear crystal for terahertz radiation generation: the image of the beam spot on the surface of the grating is created inside the crystal. Imaging errors of the conventional tilted-pulse-front THz radiation sources cause deformation of the pump pulse, namely, they result in a local elongation of the pump pulse length (see the paper by L. Pálfalvi et al., entitled “Novel setups for extremely high power single-cycle terahertz pulse generation by optical rectification”; Applied Physics Letters, Vol. 92, issue 1., pp. 171107-171109 (2008)). In case of pump beams with large cross-section (i.e. wide beams) this effect is highly detrimental to the efficiency of terahertz radiation generation. To remedy this, the above cited scientific publication proposes the use of a so-called contact grating scheme, which is free from any imaging optics and thus from imaging errors generated by the imaging optics. In this scheme the tilt of the pulse front is obtained by diffraction on a transmission optical grating formed directly (e.g. by etching) in the surface of the nonlinear crystal. The magnitude of the period of the grating to be formed (generally, in the micrometer or sub-micrometer domain) is determined by the material of the nonlinear crystal and the wavelength of the pumping. For LN and assuming a pump wavelength of typically ˜1 μm, the contact grating has to be provided with a line density of typically at least 2500-3000 l/mm (see the paper by Nagashima et al., entitled “Design of Rectangular Transmission Gratings Fabricated in LiNbO3 for High-Power Terahertz-Wave Generation”; Japanese Journal of Applied Physics, vol. 49, pp. 122504-1 to 122504-5 (2010); and the corrected paper entitled “Erratum: Design of Rectangular Transmission Gratings Fabricated in LiNbO3 for High-Power Terahertz-Wave Generation”; Japanese Journal of Applied Physics, vol. 51, p. 122504-1 (2012), as well as the paper by Ollmann et al., entitled “Design of a contact grating setup for mJ-energy THz pulse generation by optical rectification”; Applied Physics B, vol. 108, issue 4, pp. 821-826 (2012)). At the moment, preparation of an optical grating with this line density is technically not obvious, if it is possible at all. In addition, test experiments show, that if the line density of the grating exceeds a threshold value (which is about 2000 l/mm for LN), the profile of the obtained grating becomes blurred. Consequently, diffraction efficiency of the obtained grating falls greatly behind the theoretically predicted value, which results in a drastic reduction of the efficiency of terahertz radiation generation due to the highly reduced efficiency of coupling in the pump pulse.
A further significant disadvantage of the contact grating scheme lies in the fact that it is not possible to generate terahertz radiation efficiently when a plane-parallel structure is used (contrary to the statements of the aforementioned paper by Pálfalvi et al. from 2008); tilting the entry and exit planes relative to each other and providing, thus, the medium for terahertz radiation generation in the form of a prism-shaped element is unavoidable (see the above cited paper by Ollmann et al. from 2012).
The paper by Tsubouchi et al. published in the Conference Proceedings of the “41th International Conference on Infrared, Millimeter and Terahertz Waves (IRMMW-THz)” (25-30 Sep. 2016) under the title of “Compact device for intense THz light generation: Contact grating with Fabry-Perot resonator” discloses a method for generating terahertz pulses by contact grating. In order to increase the efficiency of coupling into the nonlinear crystal provided in the form of a plane-parallel element, a double coating layer acting as a Fabry-Perot resonator is formed between the surface of the crystal and the diffraction grating. Coupling out the obtained THz beam from said plane-parallel structure on the exit plane takes place in a direction other than perpendicular. This is highly disadvantageous in case of THz pulses consisting of a few cycles only and having wide bandwidth: separation of the individual spectral components makes impossible the practical utilization of the THz pulses thus obtained.
The paper by G. K. Abgaryan et al., entitled “Investigation of Parameters of Terahertz Pulses Generated in Single-Domain LiNbO3 Crystal by Step-Wise Phase Mask” (see Journal of Contemporary Physics (Armenian Academy of Sciences), vol. 51, issue 1, pp. 35-40 (2016)) teaches a scheme for generating broadband THz radiation in an LN crystal equipped with a separate step-wise prism-like phase mask. Here, the LN crystal is provided as a triangular prism that is equipped with the stepped phase mask made of a material that differs from LN. To obtain the broadband THz radiation, a pumping beam with no initial pulse front tilting is directed through the stepped phase mask to slope the amplitude front of the beam and the obtained pumping beam with a sloping intensity front is then coupled into the LN crystal to perform THz generation. To avoid diffraction distortions caused by the exciting laser pulses of the pumping beam, the mask layers corresponding to the steps of the phase mask can be separated from one another by thin mirror coatings.
The paper by Ofori-Okai et al., entitled “THz generation using a reflective stair-step echelon” (see Optics Express, vol. 24, issue 5, pp. 5057-5067 (2016)) discloses a tilted pulse front technique for terahertz radiation generation, wherein pulse front tilt of the pump beam is achieved by reflection on a stepped structure with a period of about one hundred micrometers in magnitude (a scheme using a reflection echelle grating) instead of a diffraction grating with a period falling into the micrometer domain. When being reflected, the pulse front is subject to an average tilt, whose extent is determined by the height and the width of the steps of the stair-step structure. The fine structure of the pulse front will also be stepped, the width of this fine structure is twice the width of the stepped grating, while its height will be equal to the height of the stepped grating. The pulse front tilt required by velocity matching is set by the imaging optics arranged in the propagation path of the pump pulse. The THz radiation thus generated propagates along a direction perpendicular to the envelope of the stepped pulse front within the crystal. Thus, coupling the THz radiation out of the crystal requires a prism with the same wedge angle as in the conventional scheme (see above). Consequently, especially when using wide pump beams needed for high energy terahertz radiation generation, the THz radiation obtained will be asymmetric and thus is unfit for e.g. particle acceleration.
International Publication Pamphlet No. WO 2017/081501 A2 discloses a method and a radiation source for generating terahertz radiation. The solution disclosed is obtained by combining the conventional tilted-pulse-front scheme (see above) with a contact grating. Pulse front tilting takes place preferably in two (or more) separate steps in such a way that the pulse front tilt of the pump beam is divided between the conventional setup and the contact grating. Thus, the imaging error occurring here is greatly reduced relative to that of the conventional scheme. Furthermore, according to model calculations performed for an LN crystal, advantageously a terahertz radiation generation with good efficiency can be achieved even with a line density lower (i.e. under about 2000 l/mm) than the line density needed in the simple contact grating scheme. The radiation source to accomplish the method comprises a pump source for emitting a pump pulse and a nonlinear optical medium for generating THz pulses, wherein the pump source and the nonlinear optical medium define together a light path, said pump pulse travels along this light path from the pump source to the nonlinear optical medium. There are arranged a first optical element having angular-dispersion-inducing properties and imaging optics in said light path one after the other along the propagation direction of the pump pulse. Moreover, in order to induce the pulse front tilt of the pump pulse in more than one steps, at least one further element having angular-dispersion-inducing properties is also arranged in the light path after the first element having angular-dispersion-inducing properties and the imaging optics. The medium for generating terahertz radiation is provided in the form of a prism-shaped element. As a result of dividing the pulse front tilt of the pump beam, the wedge angle of the applied prism becomes lower (γ≈30° for LN, γ≈45° for LT) than the wedge angle required by the former solutions, however, it is still large enough to result in the generation of an asymmetric beam being disadvantageous from the aspect of utilization of the terahertz radiation obtained.